Android itself is highly optimized to play media. It's a perfect base to run Kodi. LE isn't the more performant base for Kodi.
On RPi with LE you can use your TV remote, so you don't need to buy that part.
You have to buy the RPi, a case and a PSU. All in all it still could be under 50$.
Here are my instructions to install a power button and a status LED: Instructions.
This will make it work like a commercial box. Don't fear to build it.